A traditional AA filter consists of two parts, one splits the image horizontally with a ~1 pixel offset (effectively giving one image superimposed on itself with a very small horizontal offset). Behind this is a second filter that does the same vertically. The effect of this is to split each light ray four ways so some of it lands on each of the four RGGB pixels in the Bayer array.

The D800e has the first horizontal split filter but immediately behind it a second horizontal filter which combines the two images to undo the effect of the first filter. The filter material has two refractive indices for different polarizations so each incoming ray (which will contain photons with different polarization) is split into two. If the second filter has equal and opposite refractive indices, the diverged light rays are bent the other way so the they land on top of each other again, cancelling the effect of the first filter. The key point here is that the each of the superimposed images have different polarizations, allowing them to be recombined. If this weren't the case adding a second filter would produce three images not one!

As for why they do this instead of just not installing a filter, rfusca hit the nail on the head, it's much easier (and therefore cheaper) to occasionally swap a batch of vertical filters for horizontal filters when you want to build d800es than it is to disable the filter mounting part of the production line and pass the cameras through to a different AF calibration stage.

In addition to this, modern lenses are designed to correct for the refractive properties of the filter stack. Omitting the AA filter would introduce a subtle aberration into all images shot with digital era glass.